A building casts a shadow of 10 meters when the angle of elevation of the sun is

A building casts a shadow of 10 meters when the angle of elevation of the sun is 45 degrees. What is the height of the building?

A building casts a shadow of 10 meters when the angle of elevation of the sun is 45 degrees. What is the height of the building?

Correct Answer: 10 meters

Step 1: Understand that the angle of elevation is the angle between the ground and the line from the top of the building to the sun.
Step 2: Recognize that when the angle of elevation is 45 degrees, the height of the building and the length of the shadow are equal.
Step 3: Use the tangent function, which relates the height of the building to the length of the shadow: tan(angle) = height / shadow.
Step 4: Since the angle is 45 degrees, we know that tan(45) = 1.
Step 5: Substitute the values into the formula: height = shadow * tan(45).
Step 6: Calculate the height: height = 10 meters * 1 = 10 meters.

Trigonometry – The problem involves using the tangent function to relate the height of the building to the length of the shadow based on the angle of elevation.
Angle of Elevation – Understanding how the angle of elevation affects the relationship between the height of an object and the length of its shadow.